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Action-to-Action Flow Matching

Jindou Jia, Gen Li, Xiangyu Chen, Tuo An, Yuxuan Hu, Jingliang Li, Xinying Guo, Jianfei Yang

arXiv:2602.07322v2cs.ROcs.AI

TL;DR

Robotic diffusion policies face inference latency because they generate actions through repeated denoising from random noise, while existing conditioning often underuses temporal proprioceptive information. A2A instead transports historical proprioceptive actions toward future actions in latent space, achieving faster inference, broader robustness and generalization, and applicability to video generation. Its scope is narrower for discrete action dimensions and its loss weighting requires manual tuning.

  • Problem

    Diffusion-based robotic policies often rely on iterative denoising from random noise, while prevailing conditioning schemes underuse temporal proprioceptive history and can create inference-latency and generalization challenges.

  • Method

    A2A embeds historical proprioceptive action sequences into a latent space and learns an action-to-action flow that transports them to future actions instead of starting from Gaussian noise.

  • Results

    A2A matches or surpasses state-of-the-art diffusion and flow-based policies while reducing inference to fewer steps, including high-quality generation in as few as one step.

  • Takeaways & Limitations

    A2A supports efficient, temporally grounded robotic control with reported robustness to visual perturbations, generalization to unseen configurations, and extension to robotic video generation.

  • Takeaways & Limitations

    A2A is most effective for smooth continuous control, offers limited benefit for discrete or switch-like actions, and currently requires manual tuning of loss-weighting coefficients.

Abstract

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Diffusion-based policies have recently achieved remarkable success in robotics by formulating action prediction as a conditional denoising process. However, the standard practice of sampling from random Gaussian noise often requires multiple iterative steps to produce clean actions, leading to high inference latency that incurs a major bottleneck for real-time control. In this paper, we challenge the necessity of uninformed noise sampling and propose Action-to-Action flow matching (A2A), a novel policy paradigm that shifts from random sampling to initialization informed by the previous proprioceptive action. Unlike existing methods that treat proprioceptive action feedback as static conditions, A2A leverages historical proprioceptive sequences, embedding them into a high-dimensional latent space as the starting point for action generation. This design bypasses costly iterative denoising while effectively capturing the robot's physical dynamics and temporal continuity. Extensive experiments demonstrate that A2A exhibits high training efficiency, fast inference speed, and improved generalization. Notably, A2A enables high-quality action generation in as few as a single inference step, and exhibits superior robustness to visual perturbations and enhanced generalization to unseen configurations. Lastly, we also extend A2A to video generation, demonstrating its broader versatility in temporal modeling. Project site: https://lorenzo-0-0.github.io/A2A_Flow_Matching.

1 Introduction

Diffusion policies offer strong multimodal action modeling but incur latency from iterative denoising and underuse proprioceptive history. A2A initializes generation from historical proprioceptive actions, enabling efficient action-to-action flow and reported gains in speed, robustness, and generalization.

  • Diffusion policies typically require dozens of iterative denoising steps, creating a major latency bottleneck for real-time robotic control.
  • Rich proprioceptive feedback provides a structured prior about the robot’s physical state and execution history, but existing methods often use it only as static conditioning.
  • A2A uses historical proprioceptive action sequences as the generation start point, embedding them in a latent space and transporting them toward future actions.
  • A2A achieves up to 20× and 5× faster inference convergence than vanilla diffusion and flow matching, respectively, while supporting high-quality generation in one step.
  • Experiments report state-of-the-art performance across training efficiency, inference speed, visual-perturbation robustness, and generalization to unseen configurations, with an extension to robotic video generation.

2 Related work

Related work spans visuomotor policies, diffusion and flow-based generation, lightweight vision-to-action models, and strategies for optimizing diffusion initialization. A2A differs by transporting clean historical actions directly toward future actions using robotic motion continuity.

  • Visuomotor policies map high-dimensional visual inputs and low-dimensional robotic states directly to low-level control actions.
  • Diffusion policies improve multimodal action modeling through iterative generative inference, whereas lightweight vision-to-action models reduce architecture complexity but can remain vulnerable to visual distractors.
  • Prior noise-optimization methods improve diffusion initialization using learned noise mappings, warm starts, or reinforcement learning over latent-noise spaces.
  • A2A uses clean historical action data as the initial distribution, placing generation closer to future actions by exploiting physical continuity in robotic motion.

3 Action-to-action flow matching

A2A applies flow matching in a shared action-latent space, transforming historical proprioceptive actions into future actions under visual conditioning. Its aligned latent initialization, autoencoding, and consistency objectives support efficient, physically meaningful generation.

  • 3.1 Flow matching: Flow matching transforms a source distribution into a target distribution along a probability path defined by a time-dependent vector field.The formulation uses an ODE and optimal-transport interpolation between source and target states, with a neural network trained to approximate the conditional vector field.
  • 3.2 Action to action flow: A2A replaces Gaussian initialization with historical proprioceptive actions and maps their distribution directly to future actions in a shared latent space.The action representation is task-dependent: simulations use joint angles, while experiments use end-effector states.
  • 3.2 Action to action flow: The architecture encodes past actions into z0, conditions on visual features, transports z0 to z1 with a latent flow, and decodes z1 into future actions.A CNN-based autoencoder defines the action latent space, while the visual encoder and MLP produce the conditioning vector c.
  • 3.2 Action to action flow: Adjacent action chunks are similar enough that aligned latent starting and target distributions simplify transport and support strong single-step inference.The paper attributes this alignment to the physical consistency of sequential robot motions and uses a lightweight MLP for the simplified mapping.
  • 3.2 Action to action flow: Subtle noise can be added to historical actions to introduce stochasticity and improve generalization under action-level uncertainty, though dependence on preceding actions can compromise performance.The perturbation is injected before encoding and is intended to preserve a degree of multimodality.
  • 3.3 Learning objectives: A2A combines flow matching, autoencoder reconstruction, and inference consistency losses to preserve action structure and connect latent generation with executable actions.The inference consistency objective aligns ODE-inferred and ground-truth actions in latent and original action spaces; the total objective uses three positive weighting coefficients.

4 Evaluation

A2A is evaluated across simulated and real-world manipulation tasks against multiple baselines, with emphasis on training efficiency, inference cost, and generalization. The results report faster convergence, strong performance with limited data, sub-millisecond inference, and robustness to visual and configuration changes.

  • Evaluation setup: A2A is evaluated on five simulated tasks and two real-world tasks against eight state-of-the-art baselines.The simulated tasks span ManiSkill, RLBench, and LIBERO, while real-world tests use Pick Cube and Open Drawer on a Franka robot.
  • Training efficiency: A2A reaches a stable 100% success rate within 40 training epochs on Close Box, outperforming DDPM-UNet and FM-UNet in convergence speed.The training-efficiency comparison uses 100 demonstrations.
  • Training efficiency: A2A achieves 100% in-distribution success with only 30 real-world training trajectories and adapts to additional pickup locations using 10 demonstrations.The Open Drawer evaluation also reports shorter completion time, while A2A remains effective under limited-data conditions.
  • Benchmark results: Across five simulation tasks and nine algorithms, A2A consistently achieves the highest success rates.Table 1 uses 100 demonstrations and 30 training epochs.
  • Inference cost: With one-step inference, A2A exceeds 90% success after 32 training epochs, while its single-step latency reaches 0.56 ms.Beyond four inference steps, additional success-rate gains diminish substantially.
  • Generalization: A2A maintains 30–40% success on unseen randomization levels and 80% success with an unseen glowing target that causes baselines to fail.These tests assess configuration and visual generalization under distribution shifts.
  • Generalization: A2A is more sensitive to uncertainty in historical actions than noise-initialized baselines, but adding Gaussian noise with 0.1 standard deviation improves generalization.The authors identify optimal fusion of clean history and noise as an open research direction.

5 Ablation study

The ablations compare flow matching with regression and latent-space with raw-action representations. Flow matching generalizes better under perturbations, while latent-space flow matching converges better and supports strong single-step performance.

  • Regression or generation: The comparison keeps the encoder and latent-space configuration identical while replacing the flow-matching objective with deterministic regression.Flow-latent is the paper’s final flow-matching choice, whereas Reglatent is its deterministic regression counterpart.
  • Generalization capability: The study also evaluates robustness using latent-space regression and flow matching under varying environmental perturbations.Figure 10’s right panel presents the generalization comparison, while its left panel compares objectives and representation spaces.
  • Regression or generation: Flow matching and regression both achieve high success rates on the training distribution, but flow matching is more resilient to environmental perturbations.The regression variant fails to generalize to unseen scenarios.
  • Action space or latent space: Flow matching in the raw action space has inferior convergence performance compared with latent-space flow matching.The latent representation aligns the initial and target flow distributions, facilitating smoother learning.
  • Video generation: The paper extends its temporal modeling paradigm to video generation by visualizing predicted third frames in four unseen scenarios.This result is presented as a separate video-generation application rather than as part of the robotic-policy ablation.
  • Action space or latent space: Latent-space alignment enables high performance even with single-step inference.The passage attributes this capability to the structured alignment between initial and target distributions.

6 Application to video generation

The paper transfers its action-to-action temporal modeling paradigm to future video-frame prediction, introducing Frames-to-Frames flow matching. The experiment uses 100 videos for each pick-cube difficulty level from Levels 0–4.

  • Application to video generation: Frames-to-Frames flow matching transfers the A2A paradigm to future video-frame prediction, where temporal continuity is central.The paper motivates this application by relating video generation to the temporal structure of robotic manipulation.
  • Application to video generation: The video-generation training dataset contains 100 videos for each pick-cube task level from Levels 0–4.

7 Conclusion

A2A replaces noise-based initialization with action-to-action transport grounded in sequential physical consistency. Across simulation and real-world benchmarks, it matches or surpasses state-of-the-art policies with fewer inference steps and extends to video generation and other continuous temporal tasks.

  • Conclusion: A2A replaces noise-based initialization with action-to-action transport that leverages the physical consistency of sequential motions.The approach aligns starting and target distributions so a lightweight MLP can generate actions with minimal latency.
  • Conclusion: Across diverse simulation and real-world robotic benchmarks, A2A matches or surpasses state-of-the-art diffusion and flow-based policies while reducing inference to fewer steps.The conclusion characterizes this reduction as addressing the computational bottlenecks of iterative diffusion inference.
  • Conclusion: The framework is extended beyond robotics to video generation and is positioned as applicable to continuous temporal tasks.The paper describes broader scalability and future potential for domains with sequential continuity.

8 Limitation

A2A relies on physical continuity in actions, so its benefit is limited for discrete or switch-like dimensions such as binary gripper commands. The current objective also requires manual tuning of multiple loss-weighting coefficients.

  • Scope boundary: A2A is most effective for tasks dominated by smooth, continuous control signals because it relies on physical action continuity.
  • Scope boundary: For discrete or switch-like dimensions such as binary gripper open/close commands, the continuity prior provides limited benefit.
  • Training limitation: The current objective requires manual tuning of several loss-weighting coefficients.Adaptive loss weighting and support for hybrid continuous-discrete action spaces are left for future work.

A.1 Randomization level setting

The evaluation uses hierarchical randomization levels that progressively introduce object, background, lighting, and camera-viewpoint variation. Level 0 serves as the training configuration, while later levels test robustness to increasingly diverse conditions.

  • Level 0: Level 0 randomizes initial object positions and serves as the training set for evaluated algorithms.
  • Level 1: Level 1 adds environmental-background randomization to evaluate robustness against non-task-relevant visual distractors.
  • Level 2: Level 2 further randomizes illumination using varied light intensities, color temperatures, directional jitters, and positional offsets.
  • Level 3: Level 3 additionally perturbs camera extrinsics, with lateral and longitudinal shifts of ±20 cm and upward shifts from 0 to 10 cm.

A.2 Hyperparameters

The appendix standardizes model scales and reports implementation details for simulation, real-robot deployment, and video-prediction experiments. It also specifies the F2F architecture, baseline, evaluation metrics, and supplementary test settings.

  • Hyperparameters: ACT is reduced from approximately 60M parameters to match DDPM-UNet’s approximately 28M parameters for fair comparison.The Transformer backbone of ACT is halved in parameter count.
  • Real tests: A2A is deployed on a Franka platform with simulation-consistent training parameters and dual-view visual input.The dual-view setup is illustrated in Figure S1.
  • F2F architecture: F2F encodes historical frames into a 512-dimensional latent state, learns a Transformer vector field, and reconstructs future frames with convolutional upsampling.The Flow Net Transformer uses 4 layers and 4 attention heads, while reconstruction uses a 5-layer convolutional block.
  • Baseline: The F2F regression baseline keeps the same architecture while omitting the flow-matching training objective.
  • Evaluation: Video-prediction performance is evaluated with PSNR, SSIM, MSE, and LPIPS, alongside supplementary tests of training efficiency, latent convergence, and action uncertainty.The supplementary figures cover DDPM-UNet versus FM-UNet efficiency, task randomization, t-SNE latent embeddings, and multimodal navigation behavior.
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